ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of Zr2N (Materials Project id mp-1014265)

       348      107      107        0        0        0  
       107      232      163        0        0        0  
       107      163      232        0        0        0  
         0        0        0      120        0        0  
         0        0        0        0      114        0  
         0        0        0        0        0      114  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 174 GPaEV = 248.8 GPaGV = 98.6 GPaνV = 0.26168
ReussKR = 172.79 GPaER = 203.75 GPaGR = 78.155 GPaνR = 0.30348
HillKH = 173.4 GPaEH = 226.63 GPaGH = 88.377 GPaνH = 0.28217

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
69 GPa 114 GPa 114 GPa 120 GPa 218.37 GPa 524.63 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 114.09 GPa 290.03 GPa 1.5799 TPa–1 2.1037 TPa–1 34.5 GPa 120 GPa-0.0841110.71112Value
Anisotropy 2.542 1.3315 3.478Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0001
0.7071
0.7071
-0.0000
-0.0000
1.0000
0.7341
-0.0003
0.6791
0.6049
0.0002
0.7963
Axis
0.0001
0.7071
-0.7071
-0.0000
1.0000
0.0000
0.6791
-0.0007
-0.7341
-0.0002
1.0000
-0.0001
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane